Ample subvarieties and rationally connected fibrations

Under some positivity assumptions, extension properties of rationally connected fibrations from a submanifold to its ambient variety are studied. Given a family of rational curves on a complex projective manifold X inducing a covering family on a submanifold Y with ample normal bundle in X, the main results relate, under suitable conditions, the associated rational connected fiber structures on X and on Y. Applications of these results include an extension theorem for Mori contractions of fiber type and a classification theorem in the case Y has a structure of projective bundle or quadric fibration.Comment: 27 pages; v2: minor changes and corrections following the referee's comments. v3: few typos corrected. To appear in Math. An

On the cohomology of pseudoeffective line bundles

The goal of this survey is to present various results concerning the cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and related properties of their multiplier ideal sheaves. In case the curvature is strictly positive, the prototype is the well known Nadel vanishing theorem, which is itself a generalized analytic version of the fundamental Kawamata-Viehweg vanishing theorem of algebraic geometry. We are interested here in the case where the curvature is merely semipositive in the sense of currents, and the base manifold is not necessarily projective. In this situation, one can still obtain interesting information on cohomology, e.g. a Hard Lefschetz theorem with pseudoeffective coefficients, in the form of a surjectivity statement for the Lefschetz map. More recently, Junyan Cao, in his PhD thesis defended in Grenoble, obtained a general K{\"a}hler vanishing theorem that depends on the concept of numerical dimension of a given pseudoeffective line bundle. The proof of these results depends in a crucial way on a general approximation result for closed (1,1)-currents, based on the use of Bergman kernels, and the related intersection theory of currents. Another important ingredient is the recent proof by Guan and Zhou of the strong openness conjecture. As an application, we discuss a structure theorem for compact K{\"a}hler threefolds without nontrivial subvarieties, following a joint work with F.Campana and M.Verbitsky. We hope that these notes will serve as a useful guide to the more detailed and more technical papers in the literature; in some cases, we provide here substantially simplified proofs and unifying viewpoints.Comment: 39 pages. This survey is a written account of a lecture given at the Abel Symposium, Trondheim, July 201

Interacting Preformed Cooper Pairs in Resonant Fermi Gases

We consider the normal phase of a strongly interacting Fermi gas, which can have either an equal or an unequal number of atoms in its two accessible spin states. Due to the unitarity-limited attractive interaction between particles with different spin, noncondensed Cooper pairs are formed. The starting point in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory, which approximates the pairs as being noninteracting. Here, we consider the effects of the interactions between the Cooper pairs in a Wilsonian renormalization-group scheme. Starting from the exact bosonic action for the pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism with the Wilsonian approach. We compare our findings with the recent experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good agreement. We also make predictions for the population-imbalanced case, that can be tested in experiments.Comment: 10 pages, 6 figures, accepted version for PRA, discussion of the imbalanced Fermi gas added, new figure and references adde

The masterpieces of John Forbes Nash Jr.

In this set of notes I follow Nash’s four groundbreaking works on real algebraic manifolds, on isometric embeddings of Riemannian manifolds and on the continuity of solutions to parabolic equations. My aim has been to stay as close as possible to Nash’s original arguments, but at the same time present them with a more modern language and notation. Occasionally I have also provided detailed proofs of the points that Nash leaves to the reader

A five-year study on the heavy-metal pollution of Guanabara Bay sediments (Rio de Janeiro, Brazil) and evaluation of the metal bioavailability by means of geochemical speciation

Surface sediments of the Guanabara Bay (Rio de Janeiro, Brazil) were analyzed by a sequential extraction procedure for Cd, Cr, Cu, Pb, Zn, Mn and Fe, determining their distribution among five geochemical phases and in the nitric acid extractable phase. Bioavailable phases and non-bioavailable phases have been determined in six transects in the bay to define the significant level of pollution due to sediment metal contamination. A multiple correlation showed limited responsibility of Mn and Fe oxides and humic acids in the adsorption process, which allowed discrimination among the different processes and suggested the strong influence of the hydrogen sulfide present in the highly reduced bay bottom environment. The authors suggest the need to avoid disturbing bottom sediment by dredging or by artificial bottom aeration which could result in a rapid worsening of the environment due to the accelerated formation of more soluble oxygenated metal compounds making the toxic metals much more available to the benthic fauna and to the bay biota in general

Entrapment of pollutants in Mediterranean sediments and biogeochemical indicators of their impact

The transit and fate of certain pollutants (Cd, Pb, Zn and P) transported to the western Mediterranean sea-floor and a method to assess their impact are described. The spatial distribution of pollutant concentrations in the Rhone prodelta shows that their decline with distance from their source is due both to mixing with unpolluted sediments, release from contaminated particles during transit and release from sediments after deposition. Beyond the continental shelf, metals of anthropogenic origin, mainly incorporated in faecal pellets, sink and become entrapped in deep sea sediments. Because subsaturating concentrations of trace metals are often found in surface pore waters and storage, therefore, still occurs, co-precipitation with other metal ions existing in slightly supersaturated states has also to be considered. Although phosphate tends to precipitate as apatite after entering sea water, its `definitive' storage in sediments is hindered by certain forms of pollution. Low pH and reducing conditions in sediments enhance phosphate release to the overlying water . Eutrophication may then occur in localised areas. The effects of urban waste water contamination on biogeochemical processes in sediments are examined, in particular processes responsible for the transformation of organic nitrogen. Sediment quality appears to be better defined by the effectiveness of diagenetic processes than by pollutant concentration per se. In general, polluted sediments possess weak capacities to transform organic nitrogen relative to the quantities of organic matter that are available. Such sediment characteristics are indicated by the preferential growth of Caulerpa taxifolia over that of Posidonia oceanica